It might be possible to understand the formation of a chiral
condensate in the low temperature phase of QCD in terms of instantons
and the associated zero modes [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. It is
well known that there is an exact zero mode of the Dirac operator
associated with an isolated instanton or anti-instanton, and with
their finite-temperature versions known as
calorons [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}. Typical
gauge field configurations can be interpreted as a more or less dense
medium of instantons and anti-instantons. For a sufficiently high
density of topological objects, the associated zero modes will
strongly mix and form a finite band of near-zero Dirac modes, which in
turn gives rise to a finite condensate via the Banks-Casher
relation [17]}. At higher temperatures the density of
topological objects decreases, and so do the density of near-zero
Dirac modes and the chiral condensate, until the symmetry is
effectively restored. This is the “disordered medium scenario” for
chiral symmetry breaking. The mechanism of confinement is understood
less clearly, and various proposals have been put forth: we invite the
interested reader to consult
Refs. [18]}, [19]}.
